I know the OP has updated to say she isn’t going, but just wanted to say it can work. To be fair to the bride, before you have kids it’s easy to not comprehend at all how difficult everything is. It depends on how good a friend she is and how much you want to be there. I was Best Man to my friend when my firstborn was 6 weeks old. 3 hour drive away in central London hotel. My parents came along and stayed in the hotel in a room next to ours, so they spent the day in a lovely hotel room with the baby and it all went fine. Breastfeeding was really hard to start with and a real struggle. By 6 weeks though I was doing a mix of breastfeeding and expressing and the baby taking that in a bottle. I was fortunate that she would switch between both happily (some babies do not) so for the duration of the wedding my parents had expressed milk to give her lined up ready in the hotel room fridge. I didn’t feed her directly during the day, she was a really slow feeder from the breast and I would have been away from the wedding for a couple of hours at at time if I’d tried to breastfeed her. I did have to go and express in my room every few hours as you get very engorged quite quickly and it’s mightily uncomfortable so had to plan that in, plus taking all my sterilizing stuff etc etc and storing the newly expressed milk. It was a bit of a faff, a bit of a milk production/sterilizing bottles production line at times and took some planning, and willing parents! but we did make it work. Being in the actual venue made it a lot easier though, a 10 minute drive is not as convenient as popping up to a hotel room and takes a big chunk out of the day for each visit to check/feed.
My friend put no pressure on me to be his best man, and would have understood if I’d declined in the circumstances, unlike the bride in this instance. I agreed with the naivety of someone who really didn’t understand the reality of having a baby though and was confident 6 weeks in I’d be fine!
We took the same baby to my husbands sisters wedding at 3 weeks, 2 hour drive away, I’d had 45 minutes sleep the night before (and most nights leading up) as the baby was completely nocturnal for the first month. baby exclusively breastfeeding at that point, both of us really rubbish at it, nightmare long feeds, both us totally shellshocked at the whole change in our lives over the previous 3 weeks. I can not believe I went, I was a husk of a woman still recovering from a traumatic birth and trying to establish breastfeeding. Three weeks to the next wedding made a big difference, but there are just no guarantees or knowing how you personally will be 6 weeks after birth. At the very least you need an accommodating, understanding friend willing to accept you might need some flexibility around the wedding, and it doesn’t sound like the bride is. (You also need amazing parents, which fortunately it sounds like the OP does have!)
Could you arrange to all stay in the wedding venue, or give a provisional yes, but tell her if things aren’t going to plan you may have to pull out and see how you and baby are a couple of weeks before the big day? I know when planning a wedding that’s not fabulous, but realistically people pull out on the day with sickness and give even less notice. We had about 6 people who couldn't get to our wedding on the day due to being snowed in, including a heavily pregnant friend who tried but her car started skidding when they tried to leave the house! We were all gutted they didn’t make it, but you have to be reasonably realistic.
My final thing about the wedding at 6 weeks - I had some dark and exhausting moments with my firstborn and was overwhelmed by everything for a long time. But at that wedding, over the initial shock and getting the hang of it a bit, I had a great time. It was nice to wear some proper clothes and catch up with friends and eat a really nice (hot!) meal whilst my parents held the fort/baby and I took a much needed mental/physical break for the day. It took effort and planning and I was lucky to be well enough, and I’m glad I was there for my friend on the day.
I absolutely did not make it to the stag do at 2 weeks post-partum though!